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The goal of the current text is to study non-archimedean analytic derived de Rham cohomology by means of formal completions. Our approach is inspired by the deformation to the normal cone provided in \cite{Gaitsgory_Study_II}. More…

The 2-surface characterization of special classical radiative Higgs-, Yang-Mills and linear zero-rest-mass (l.z.r.m) fields with any spin is investigated. We determine all the zero quasi-local mass Higgs- and Yang-Mills field configurations…

We consider {\em discretized} Hamiltonian PDEs associated with a Hamiltonian function that can be split into a linear unbounded operator and a regular nonlinear part. We consider splitting methods associated with this decomposition. Using a…

We present a criterion for the stochastic completeness of a submanifold in terms of its distance to a hypersurface in the ambient space. This relies in a suitable version of the Hessian comparison theorem. In the sequel we apply a…

For $h$-FEM discretisations of the Helmholtz equation with wavenumber $k$, we obtain $k$-explicit analogues of the classic local FEM error bounds of [Nitsche, Schatz 1974], [Wahlbin 1991], [Demlow, Guzm\'an, Schatz 2011], showing that these…

In this note, we continue the investigation of a projective K\"ahler manifold $M$ of semi-negative holomorphic sectional curvature $H$. We introduce a new differential geometric numerical rank invariant which measures the number of linearly…

Pseudo-holomorphic curves on almost complex manifolds have been much more intensely studied than their "dual" objects, the plurisubharmonic functions. These functions are defined classically by requiring that the restriction to each…

In this paper we study wave propagation and scattering near a rotating black hole. In particular, we assume a coherent emission source near the black hole and investigate the wavefront distortion as seen by a distant observer. Near the…

Quasi-analytic wave-front sets of distributions which correspond to the Gevrey sequence $p!^s$, $s\in[1/2,1)$ are defined and investigated. The propagation of singularities are deduced by considering sequences of Gaussian windowed…

The classical Pfaff-Darboux theorem, which provides local 'normal forms' for $1$-forms on manifolds, has applications in the theory of certain economic models [Chiappori P.-A., Ekeland I., Found. Trends Microecon. 5 (2009), 1-151]. However,…

Let $K$ be the fraction field of a two-dimensional henselian, excellent, equi-characteristic local domain. We prove a local-global principle for Galois cohomology with finite coefficients over $K$. We use classical machinery from \'etale…

In this paper, we introduce the notion of standard homogeneous $(\alpha_1,\alpha_2)$-metrics, as a natural non-Riemannian deformation for the normal homogeneous Riemannian metrics. We prove that with respect to the given bi-invariant inner…

Quasinormal frequencies of electromagnetic and gravitational perturbations in asymptotically AdS spacetime can be identified with poles of the corresponding real-time Green's functions in a holographically dual finite temperature field…

We explore wave-mechanical scattering in two spatial dimensions assuming that the corresponding potential is invariant under linear symmetry transforms such as rotations, reflections and coordinate exchange. Usually the asymptotic…

Contrast functions play a fundamental role in information geometry, providing a means for generating the geometric structures of a statistical manifold: a pseudo-Riemannian metric and a pair of torsion-free conjugate affine connections.…

Almost hypercomplex manifolds with Hermitian and anti-Hermitian metrics are considered. A linear connection $D$ is introduced such that the structure of these manifolds is parallel with respect to D. Of special interest is the class of the…

We establish a criterion on wrapped Floer homology of an exact Lagrangian sub- manifold in a Liouville domain, which ensures the almost-existence of Hamiltonian chords near a given energy level. To this purpose we introduce a relative…

We prove that every Kaehler metric, whose potential is a function of the time-like distance in the flat Kaehler-Lorentz space, is of quasi-constant holomorphic sectional curvatures, satisfying certain conditions. This gives a local…

We develop a semiclassical second microlocal calculus of pseudodifferential operators associated to linear coisotropic submanifolds $\mathcal{C}\subset T^* \mathbb{T}^n$, where $\mathbb{T}^n = \mathbb{R}^n / \mathbb{Z}^n$. First…

The (pseudo-)Riemann-metrizability and Ricci-flatness of Finsler spaces with $m$-Kropina metric $F = \alpha^{1+m}\beta^{-m}$ of Berwald type are investigated. We prove that the affine connection on $F$ can locally be understood as the…